That explanation sounds bogus. I'd guess that our sport is called "football" simply because in origin, in the mid-19th century, it was precious little different from what's now known as rugby or Oz-rules football. The differences we see in the modern games arose well after the name was established.

Besides, we won that little insurrection in the late 1700's. We could name a sport "Your Mom's Hairy Ass" if we wanted, but:a) the name's already taken by a picnic game, andb) the etymology would be just about a bitch to explain.